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Competitive exploration of rectilinear polygons

Mikael Hammar, Bengt J. Nilsson, Mia Persson
2006 Theoretical Computer Science  
We prove constant competitive strategies and lower bounds for exploring a simple rectilinear polygon in the L 1 metric.  ...  Exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem.  ...  Conclusions We have presented constant competitive strategies and lower bounds to explore a rectilinear simple polygon in the L 1 metric with one or more robots.  ... 
doi:10.1016/j.tcs.2005.11.032 fatcat:bfuyjcmn45e4fdnxw5eei34nna

Optimality and competitiveness of exploring polygons by mobile robots

Jurek Czyzowicz, Arnaud Labourel, Andrzej Pelc
2011 Information and Computation  
For competitiveness the situation is more optimistic: we show a competitive exploration algorithm for rectilinear polygons whenever the sensing area is a square, for both tasks, regardless of the metric  ...  Most of our results concern rectilinear polygons.  ...  For the problem of competitiveness of on-line exploration of rectilinear polygons, our results are less complete: we showed a competitive algorithm for a robot with square sensing area, regardless of the  ... 
doi:10.1016/j.ic.2010.09.005 fatcat:ofqgtwbrxjg3fgtbnglm3s7rwa

Optimality and Competitiveness of Exploring Polygons by Mobile Robots [chapter]

Jurek Czyzowicz, Arnaud Labourel, Andrzej Pelc
2009 Lecture Notes in Computer Science  
For competitiveness the situation is more optimistic: we show a competitive exploration algorithm for rectilinear polygons whenever the sensing area is a square, for both tasks, regardless of the metric  ...  Most of our results concern rectilinear polygons.  ...  For the problem of competitiveness of on-line exploration of rectilinear polygons, our results are less complete: we showed a competitive algorithm for a robot with square sensing area, regardless of the  ... 
doi:10.1007/978-3-642-04128-0_23 fatcat:oyvam5vi7vfo5byd7djoxn7ir4

Polygon Exploration with Time-Discrete Vision [article]

Sandor P. Fekete, Christiane Schmidt
2010 arXiv   pre-print
a matching upper bound by providing an O(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.  ...  , a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give  ...  Difficulties of Discrete Vision The main result of this paper is to develop an exploration strategy for simple rectilinear polygons.  ... 
arXiv:0807.2358v2 fatcat:ej2a5yrhlrg3fernvpoahzlapq

Online Vertex Exploration Problems in a Simple Polygon

Yuya HIGASHIKAWA, Naoki KATOH
2013 IEICE transactions on information and systems  
We also study the case of a rectilinear simple polygon, and give a 1.167-competitive algorithm.  ...  The information of the polygon is given online. As the exploration proceeds, the searcher gains more information of the polygon. We give a 1.219-competitive algorithm for this problem.  ...  Competitive Analysis for Rectilinear Polygon In this section, we analyze the competitive ratio of AOE for a rectilinear polygon (see Fig. 11 ).  ... 
doi:10.1587/transinf.e96.d.489 fatcat:2gl6k5smpbdqzezpghzbr3s5nu

Polygon exploration with time-discrete vision

Sándor P. Fekete, Christiane Schmidt
2010 Computational geometry  
a matching upper bound by providing an O (log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.  ...  , a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give  ...  Difficulties of time-discrete vision The main result of this paper is to develop an exploration strategy for simple rectilinear polygons.  ... 
doi:10.1016/j.comgeo.2009.06.003 fatcat:agedksm4v5hw5k4aup6s3nmlhu

Page 2058 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
The main result of the paper is a competitive strategy in the L; metric for exploring rectilinear polygonal rooms with a bounded number of rectilinear polygonal obstacles.  ...  In particular, the authors give a polynomial-time off- line algorithm for exploring simple rectilinear polygons in the L, metric.  ... 

Exploring the Outer Boundary of a Simple Polygon

Qi WEI, Xiaolin YAO, Luan LIU, Yan ZHANG
2021 IEICE transactions on information and systems  
We investigate an online problem of a robot exploring the outer boundary of an unknown simple polygon P. The robot starts from a specified vertex s and walks an exploration tour outside P.  ...  We consider P in two scenarios: convex polygon and concave polygon. For the first scenario, we prove a lower bound of 5 and propose a 23.78-competitive strategy.  ...  [11] studied the exploration of rectilinear polygon without holes under discrete visibility. They showed an O(logA)-competitive strategy, where A is the aspect ratio of the polygon. Premkumar et al  ... 
doi:10.1587/transinf.2020edp7234 fatcat:vz633deiszfupk2kcsk3inffty

Competitive searching in a generalized street

Amitava Datta, Christian Icking
1999 Computational geometry  
We present an on-line strategy for a robot to find the target in an unknown rectilinear G-street; the length of its path is at most 9 times the length of the shortest path in the L 1 metric, and 9.06 times  ...  We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far.  ...  Other interesting geometric applications for competitive strategies are e. g. the search for the kernel of a polygon [15, 24, 28, 22] , exploration or path planning in unknown environments [7, 11, 12  ... 
doi:10.1016/s0925-7721(99)00015-2 fatcat:r7pol4ppbzbg5exo7ujkld6jfy

Competitive searching in a generalized street

Amitava Datta, Christian Icking
1994 Proceedings of the tenth annual symposium on Computational geometry - SCG '94  
We present an on-line strategy for a robot to find the target in an unknown rectilinear G-street; the length of its path is at most 9 times the length of the shortest path in the L 1 metric, and 9.06 times  ...  We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far.  ...  Other interesting geometric applications for competitive strategies are e. g. the search for the kernel of a polygon [15, 24, 28, 22] , exploration or path planning in unknown environments [7, 11, 12  ... 
doi:10.1145/177424.177622 dblp:conf/compgeom/DattaI94 fatcat:xqspvtsb55agrckbmk47t6uqjy

Competitive Online Approximation of the Optimal Search Ratio [chapter]

Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, Gerhard Trippen
2004 Lecture Notes in Computer Science  
We answer these questions for simple polygons and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor.  ...  There is also a polynomial time 8-search-competitive offline search algorithm. Proof. For a rectilinear simple polygon, P , Papadimitriou et al.  ...  Even for rectilinear simple polygons no polynomial time algorithm for the optimal search path is known, but we can find better online algorithms: Theorem 13 For an agent with vision in a simple rectilinear  ... 
doi:10.1007/978-3-540-30140-0_31 fatcat:hmcx46y6qrhlbisxmgahbbv25u

Competitive Online Approximation of the Optimal Search Ratio

Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, Gerhard Trippen
2008 SIAM journal on computing (Print)  
We answer these questions for simple polygons and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor.  ...  There is also a polynomial time 8-search-competitive offline search algorithm. Proof. For a rectilinear simple polygon, P , Papadimitriou et al.  ...  Even for rectilinear simple polygons no polynomial time algorithm for the optimal search path is known, but we can find better online algorithms: Theorem 13 For an agent with vision in a simple rectilinear  ... 
doi:10.1137/060662204 fatcat:46hnlkwgzne3lc4ertgvipx6ji

Page 2079 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Hans-Dietrich Hecker (Jena) 2003¢:68234 68U05 68T40 Hammar, Mikael (I-SLRN-IA2; Baronissi); Nilsson, Bengt J.; Schuierer, Sven (D-FRBG-I; Freiburg) Improved exploration of rectilinear polygons.  ...  The following problem is considered: Given a rectilinear polygon, a point-sized robot has to construct a map of it without a priori knowledge of the environment.  ... 

Walking in Streets with Minimal Sensing [chapter]

Azadeh Tabatabaei, Mohammad Ghodsi
2013 Lecture Notes in Computer Science  
We also consider a special case of the problem in which the street is rectilinear and the search path has to be rectilinear.  ...  We offer a data structure similar to Gap Navigation Tree to maintain the essential sensed data of the explored street.  ...  Introducing more general classes of polygons which admit a competitive searching with a minimal sensing model is an interesting open problem.  ... 
doi:10.1007/978-3-319-03780-6_32 fatcat:7bjlzeclofeo5pgsm3ptr7v6dm

Page 2381 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
For the problem of exploring a simple rectilinear polygon (under the L; norm), Deng, Kameda, and Papadimitriou gave a 2-competitive deterministic algorithm; we present a randomized exploration al- gorithm  ...  Summary: “We consider a number of search and exploration prob- lems from the perspective of robot navigation in a simple polygon.  ... 
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